Title

Author

Defense Date

Document Type

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

David J. Edwards

Second Advisor

QiQi Lu

Third Advisor

D'arcy P. Mays

Fourth Advisor

Yongjia Song

Fifth Advisor

Peter A. Parker

Abstract

The success of screening experiments hinges on the effect sparsity assumption, which states that only a few of the factorial effects of interest actually have an impact on the system being investigated. The development of a screening methodology to harness this assumption requires careful consideration of the strengths and weaknesses of a proposed experimental design in addition to the ability of an analysis procedure to properly detect the major influences on the response. However, for the most part, screening designs and their complementing analysis procedures have been proposed separately in the literature without clear consideration of their ability to perform as a single screening methodology.

As a contribution to this growing area of research, this dissertation investigates the pairing of non-replicated and partially–replicated two-level screening designs with model selection procedures that allow for the incorporation of a model-independent error estimate. Using simulation, we focus attention on the ability to screen out active effects from a first order with two-factor interactions model and the possible benefits of using partial replication as part of an overall screening methodology. We begin with a focus on single-criterion optimum designs and propose a new criterion to create partially replicated screening designs. We then extend the newly proposed criterion into a multi-criterion framework where estimation of the assumed model in addition to protection against model misspecification are considered. This is an important extension of the work since initial knowledge of the system under investigation is considered to be poor in the cases presented. A methodology to reduce a set of competing design choices is also investigated using visual inspection of plots meant to represent uncertainty in design criterion preferences. Because screening methods typically involve sequential experimentation, we present a final investigation into the screening process by presenting simulation results which incorporate a single follow-up phase of experimentation. In this concluding work we extend the newly proposed criterion to create optimal partially replicated follow-up designs. Methodologies are compared which use different methods of incorporating knowledge gathered from the initial screening phase into the follow-up phase of experimentation.